Dimensional collapse and fractal attractors of a system with fluctuating delay times

TL;DR

This paper investigates delay systems with fluctuating delay times, revealing that such fluctuations cause a collapse in system dimension and produce fractal attractors, contrasting with typical fuzzy attractors in random systems.

Contribution

It introduces the concept of dimensional collapse and fractal attractors in delay systems with variable delay times, highlighting their unique dynamical properties.

Findings

Delay fluctuations lead to a collapse in system dimension.

Attractors become fractal due to delay variability.

Contrasts with fuzzy attractors in other random systems.

Abstract

A frequently encountered situation in the study of delay systems is that the length of the delay time changes with time, which is of relevance in many fields such as optics, mechanical machining, biology or physiology. A characteristic feature of such systems is that the dimension of the system dynamics collapses due to the fluctuations of delay times. In consequence, the support of the long-trajectory attractors of this kind of systems is found being fractal in contrast to the fuzzy attractors in most random systems.